Have you ever checked a trip planner app that told you the bus was coming in 10 minutes. You raced to get to the stop only to find out that your bus was running either 2 minutes early or 10 minutes late. We regularly commute via public transit and have experienced this over and over again. Typically we'd like to do something else with our time than to wait at the stop, like picking up a coffee or take another bus more likely to bring us quicker to our destination. What if we could better decide when we have to show up by taking into account the probability for when the bus will arrive?


The Valley Transportation Authority (VTA) here in the Bay Area provides predictions about the departure time of transit vehicles. However, the exact expected departure times are usually uncertain. They can truly only be predicted to the minute in limited circumstances, such as shortly before arrival and when the traffic is stable. Arrival times are better represented as a probability distribution. But how can this information be shared with commuters so they can make better decisions?


We propose providing commuters with multiple possible arrival times for transit that could be delayed or running hot ahead of their schedule:

  1. Optimistic: The earliest time the transport could arrive. This is when you should be at the station if you want to be absolutely certain to catch the bus before it departs. Color: Green.
  2. Realistic: When is a good time to be at the stop with a high likelihood that you won't miss the bus. Color: Orange.
  3. Pessimistic: When the bus will arrive if it is really late, like a one-in-a-hundred arrivals delayed. Color: Red.


We used a neural network trained on collected/historical departure times to generate probability distributions of transit delays. We created a demonstration for the VTA to show how their Real Time Information displays can provide more granular information about arrival time probabilities to commuters. The concept can be used to extend the VTA Real Time Information into the future by applying the probability distribution of arrival times.

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